st: an estimation method question

We are trying to estimate an equation which has some constraints by
observation. We are studying founders of firms. The dependent variable
is the share of the firm. We are studying what factors influence the
shares. We now have a problem: for each firm, the shares necessarily
sum to one. We were thinking of dropping an observation per firm, but
it turns out the results are dependent on which observation to drop.
Any suggestions on estimation methods would be helpful.